A number of processes have already been investigated for their preparation (J. Am. Oil Chem. Soc. 48, 657 (1971)). U.S. Pat. No. 1,881,172 and U.S. Pat. No. 2,821,535 describe the reaction of Na isethionate with fatty acid chlorides. This reaction requires the use of absolutely dry and finely powdered Na isethionate; in addition, the preparation of the fatty acid hall des from fatty acid and phosphorus trichloride is time-consuming and costly and is associated with the unavoidable production of phosphorous acid. If undistilled acid chloride is used, the final product is usually contaminated by phosphorus-containing compounds, which can lead to odor problems. Direct condensation of Na isethionate with fatty acids requires reaction temperatures of 220.degree.-250.degree. C. It is usually necessary to employ an excess of fatty acid in order to complete this reaction, The reaction can be carried out without a catalyst (DE 1,121,045) and the presence of zinc oxide (U.S. Pat. No. 3,320,292), zinc salts of organic acids (U.S. Pat. No. 4,405,526), boric acid (U.S. Pat. No. 2,923,724) or phosphorus-containing acids (U.S. Pat. No. 3, 004,049 ). When gaseous hydrogen chloride is used as the catalyst, direct esterification is possible even at 180.degree. C. (U.S. Pat. No. 3,167,570). According to U.S. Pat. No. 3,151,136, esterification of free isethionic acid using fatty acid takes place even at 130.degree. C., but the industrial preparation of free isethionic acid from its easily accessible salts, and the neutralization of the condensation products present difficulties. The object of the present invention is to provide a process for the preparation of salts of acyloxyalkanesulfonic acids which is easy to carry out, even on a large industrial scale, and in which a direct condensation can be carried out, even under mild reaction conditions, starting from salts of hydroxyalkanesulfonic acids and fatty acids.